Abstract
Suppose l=2m+1, m>0. We introduce m "theta-series", [1],...,[m], in Z/2[[x]].
It has been conjectured that the n for which the coefficient of x^n in 1/[i] is
1 form a set of density 0. This is probably always false, but in certain cases,
for n restricted to certain arithmetic progressions, it is true. We prove such
zero-density results using the theory of modular forms, and speculate about
what may be true in general.